Question

A firm wants a sustainable growth rate of 2.78 percent while maintaining a dividend payout ratio of 20 percent and a profit margin of 4 percent. The firm has a capital intensity ratio of 2. What is the debt–equity ratio that is required to achieve the firm's desired rate of growth?

Multiple Choice

• .80 times

• .69 times

• .85 times

• .31 times

• .16 times

Answer 1

Answer is “0.69 times”

Retention Ratio, b = 1 - Dividend Payout Ratio
Retention Ratio, b = 1 - 0.20
Retention Ratio, b = 0.80

Sustainable Growth Rate = [ROE * b] / [1 - ROE * b]
0.0278 = [ROE * 0.80] / [1 - ROE * 0.80]
0.0278 - ROE * 0.02224 = ROE * 0.80
0.0278 = ROE * 0.82224
ROE = 0.03381 or 3.381%

ROE = Profit Margin * Equity Multiplier / Capital Intensity Ratio
0.03381 = 0.04 * Equity Multiplier / 2.00
Equity Multiplier = 1.69

Equity Multiplier = 1 + Debt-Equity Ratio
1.69 = 1 + Debt-Equity Ratio
Debt-Equity Ratio = 0.69